zbMATH — the first resource for mathematics

Decomposition matrices for spin characters of symmetric groups. (English) Zbl 0651.20007
Let \(\tilde S_ n\) be a double cover of the symmetric group \(S_ n\). The faithful irreducible characters of \(\tilde S_ n\) are called spin characters. In this paper a study of the p-decomposition numbers of such characters is initiated for odd prime integers p. A general technique is developed by a non-trivial modification of a corresponding technique for the characters of \(S_ n\). Then the decomposition numbers are determined explicitly for \(p=3\) and \(3\leq n\leq 11\) with an ambiguity for \(n=9\). The second author will deal separately with the cases \(p=5,7,11\).
Reviewer: J.B.Olsson

20C30 Representations of finite symmetric groups
20C20 Modular representations and characters
20C25 Projective representations and multipliers
Full Text: DOI
[1] DOI: 10.1016/0021-8693(79)90304-1 · Zbl 0433.20010 · doi:10.1016/0021-8693(79)90304-1
[2] DOI: 10.1515/crll.1911.139.155 · JFM 42.0154.02 · doi:10.1515/crll.1911.139.155
[3] DOI: 10.1017/S030500410006388X · Zbl 0591.20010 · doi:10.1017/S030500410006388X
[4] DOI: 10.1112/jlms/s2-33.3.441 · Zbl 0633.20007 · doi:10.1112/jlms/s2-33.3.441
[5] DOI: 10.1112/plms/s3-12.1.55 · Zbl 0104.25202 · doi:10.1112/plms/s3-12.1.55
[6] Macdonald, Symmetric Functions and Hall Polynomials (1979) · Zbl 0487.20007
[7] James, The Representation Theory of the Symmetric Group (1981)
[8] DOI: 10.4153/CJM-1965-055-0 · Zbl 0135.05602 · doi:10.4153/CJM-1965-055-0
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.